A variational approach to moving contact line hydrodynamics

In immiscible two-phase flows, the contact line denotes the intersection of the fluid–fluid interface with the solid wall. When one fluid displaces the other, the contact line moves along the wall. A classical problem in continuum hydrodynamics is the incompatibility between the moving contact line...

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Bibliographic Details
Published in:Journal of fluid mechanics 2006-10, Vol.564, p.333-360
Main Authors: QIAN, TIEZHENG, WANG, XIAO-PING, SHENG, PING
Format: Article
Language:English
Subjects:
Boundary conditions
Energy dissipation
Exact sciences and technology
Fluid dynamics
Fluid mechanics
Fundamental areas of phenomenology (including applications)
Hydrodynamics
Multiphase and particle-laden flows
Nonhomogeneous flows
Physics
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Summary:In immiscible two-phase flows, the contact line denotes the intersection of the fluid–fluid interface with the solid wall. When one fluid displaces the other, the contact line moves along the wall. A classical problem in continuum hydrodynamics is the incompatibility between the moving contact line and the no-slip boundary condition, as the latter leads to a non-integrable singularity. The recently discovered generalized Navier boundary condition (GNBC) offers an alternative to the no-slip boundary condition which can resolve the moving contact line conundrum. We present a variational derivation of the GNBC through the principle of minimum energy dissipation (entropy production), as formulated by Onsager for small perturbations away from equilibrium. Through numerical implementation of a continuum hydrodynamic model, it is demonstrated that the GNBC can quantitatively reproduce the moving contact line slip velocity profiles obtained from molecular dynamics simulations. In particular, the transition from complete slip at the moving contact line to near-zero slip far away is shown to be governed by a power-law partial-slip regime, extending to mesoscopic length scales. The sharp (fluid–fluid) interface limit of the hydrodynamic model, together with some general implications of slip versus no slip, are discussed.
ISSN:0022-1120
1469-7645
DOI:10.1017/S0022112006001935